Which is the equation of an ellipse with directrices at x = ±4 and foci at (2, 0) and (−2, 0)?

B

Step-by-step explanation:

Know the vocabulary for algebraic fractions. The following terms will be used throughout the examples, and are common in problems involving algebraic fractions:

Numerator: The top part of a fraction (ie. (x+5)/(2x+3)).

Denominator: The bottom part of the fraction (ie. (x+5)/(2x+3)).

Common Denominator: This is a number that you can divide out of both the top and bottom of a fraction. For example, in the fraction 3/9, the common denominator is 3, since both numbers can be divided by 3.

Factor: One number that multiples to make another. For example, the factors of 15 are 1, 3, 5, and 15. The factors of 4 are 1, 2, and 4.

Simplified Equation: This involves removing all common factors and grouping similar variables together (5x + x = 6x) until you have the most basic form of a fraction, equation, or problem. If you cannot do anything more to the fraction, it is simplified.

Review how to solve simple fractions. These are the exact same steps you will take to solve algebraic fractions.[1] Take the example, 15/35. In order to simplify a fraction, we need to find a common denominator. In this case, both numbers can be divided by five, so you can remove the 5 from the fraction:

15 → 5 * 3

35 → 5 * 7

Now you can cross out like terms. In this case you can cross out the two fives, leaving your simplified answer, 3/7.

Remove factors from algebraic expressions just like normal numbers.[2] In the previous example, you could easily remove the 5 from 15, and the same principle applies to more complex expressions like, 15x – 5. Find a factor that both numbers have in common. Here, the answer is 5, since you can divide both 15x and -5 by the number five. Like before, remove the common factor and multiply it by what is “left.”

15x – 5 = 5 * (3x – 1)

To check your work, simply multiply the five back into the new expression – you will end up with the same numbers you started with.

I hope this helped : )

answer: it's upside down and i can't read it

step-by-step explanation:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.